Regression or clustering?

I do have a dataset related to a ticket resolution system with different ticket categories.

I am asked to predict the -time to resolution- for each ticket being the target value available in the training set only for the tickets marked as resolved. Which is the model to be applied to predict the continue value (time to resolution) as I do not have a label for all the data but just for a category subset?

i.e. ticket on open status do not have a “time to resolution”

hi
CAN YOU SHARE YOUR GLIMPSES OF DATA SET HERE.
THANKS

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